"How did you happen to be so good with fractions," friends used to ask when I was in middle school. Everybody knows everybody universally dislikes fractions. For me, it was all about distance swimming. I knew I could solve the world's problems during a long workout (though I'd forget the solutions to the world's most serious problems as I climbed out of the water); what I didn't know was how I was using swimming to solidify my working facility with fractions. It was simple: as I swam 1,000 meters, I was constantly figuring out what fractions -- and what ratios were identical to the reduced fractions -- could represent how far I had swum and how much further I had to swim before I finished. It started simply: if I swam 40 lengths in a 25 meter pool, then after 7 lengths, I was 7/40th done and had 33/40 to go.
Sometimes, however, I swam in the 20 meter YMCA pool and the numbers became different. I needed to focus and not just rely on memory. I now had to swim 50 lengths to complete 1,000 meters.
My thinking soon became more complicated and required swifter calculations -- I moved to measuring what fraction of the swim I had completed for each stroke -- or even each partial stroke.
Bored with that, I began watching my teammates swimming in the neighboring lanes. What were their ratios and how were their numbers different from mine? At what points would we pass each other?
I long since moved away from my home town, stopped swimming, and became a math teacher. I forgot about fractions in the fast lane.
Then deep into middle age, I started swimming again. And calculating fractions. I kept this secret lest my lane-mates think me insane.
I don't always swim in pools. There are lakes with cool fresh water, sunbeams that cut through the waves, and no visible bottoms. Plants grow through the water towards the source of the sunbeams, branching in infinitely smaller "Y" shapes at the same angles. Bubbles surface and break into more and smaller bubbles from the depths; there are no numbers. Only fractals. And chaos. And new things to think about.
Your blog: where do you use math in secret? Or if you don't use math in secret, where might you start using math in secret or not in secret so you can increase your skills in math?
